Lured by the Consensus

Roni Michaely, Amir Rubin, Dan Segal, and Alexander Vedrashko*

Abstract: We find that investors are fixated on analysts’ consensus outputs (earnings forecasts, recommendations,

and forecast dispersion), which can be inferior signals compared to the corresponding outputs provided by

high-quality analysts, especially when a large number of high-quality analysts follow the firm. This result,

which holds at the firm and market level, implies inefficient use of the information contained in analysts’

outputs. Further, the post-earnings announcement drift (PEAD) phenomenon occurs only when high-quality

analysts are more uncertain about the firm’s performance than all analysts following the firm. We conclude

that the market’s fixation on consensus measures has significant negative economic implications.

Keywords: consensus, analyst quality, forecasts, post-earnings announcement drift, stock

recommendations

JEL: G10; G11; G14; G17; G24; M41

*Michaely is from The Geneva Finance Research Institute, University of Geneva, (roni.michaely@unige.ch). Rubin

is from Simon Fraser University and IDC (arubin@sfu.ca). Segal is from IDC and Singapore Management University

(dsegal@idc.ac.il). Vedrashko is from Simon Fraser University (awv@sfu.ca). We thank the discussants and seminar

participants at the AsianFA meeting in Tokio, EFMA meeting in Milan, FIRS meeting in Barcelona, MFS meeting in

Budapest, Hebrew University, Tel-Aviv University, University of Connecticut, and University of Vienna for helpful

comments and suggestions.

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Analysts are recognized as important information providers in financial markets. Investors

and academics alike use analysts’ consensus earnings forecasts as a measure of the market

expectations of firms’ future earnings. The perceived importance of the consensus forecast has

increased in recent years to the extent that even companies’ investor relations departments follow

the consensus on a continuous basis (Consensus earnings estimates report, 2013). Consensus

analysts’ recommendations have also become readily and, often, freely available for investors,

e.g., on the Nasdaq website. However, by construction, the consensus ignores the possibility that

analysts have different abilities and information sets, resulting in varying levels of forecast

accuracy and recommendation quality that are persistent over time.1

Thus, fixation on the consensus can have negative economic implications: investors may

be missing information and incur opportunity costs if they focus on the consensus and disregard

the heterogeneity in analyst quality. On the other hand, using the single number of the consensus

instead of differentiating among analysts can be optimal for investors. A simple average construct

can achieve a better level of predictability than more complex models that incorporate quality

differences (e.g., a literature review in Clemen, 1989); for example, the highest quality analyst’s

forecast can be less accurate than the consensus forecast, which diversifies individual errors.2 Even

if some analysts are consistently more accurate than the consensus, the costs of gathering

information and spending cognitive effort on identifying analysts with superior ability may exceed

1 Individual analysts’ forecast accuracy systematically differs for reasons including analysts’ varying experience

(Mikhail, Walther, and Willis, 1997; Clement, 1999; Hirst, Hopkins, and Wahlen, 2004), aptitude (Jacob, Lys and

Neale, 1999), education (Maines, McDaniel, and Harris, 1997; De Franco and Zhou, 2009), brokerage house

association and underwriting relationships (Lin and McNichols, 1998; Clement, 1999), proximity to the firm (Malloy,

2005), lead analyst and star status categorization (Stickel, 1992; Cooper, Day, and Lewis, 2001), or work habits

(Rubin, Segal, and Segal, 2017). 2 For example, consider a firm followed by four analysts, whose rankings in terms of forecast accuracy are perfectly

persistent over time. Let the top analyst’s forecast error (the analyst’s forecast minus actual earnings per share) be 2¢,

and the remaining three analysts have forecast errors of -4¢, -5¢, and 8¢. The consensus forecast error is 0.25¢, less

than the forecast error of the most accurate analyst and that of the average forecast of analysts in the top half of the

ranking, who can be called high-quality analysts. Since the persistence of analysts’ forecast accuracy is less than

perfect in actual markets, relying on the consensus forecast can make even more sense for investors.

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the economic benefits of going beyond the consensus, such as when analyst quality heterogeneity

is small. In fact, investors’ fixation on the mean of analysts’ forecast distribution can be an instance

of central fixation bias, which describes people’s natural tendency to fixate their vision at the center

of a group of objects and which can be optimal for initial information processing (Tatler, 2007).

Hence, our objectives are two-fold. We first assess whether investors mainly focus on the

consensus output. Second, we examine whether analysts’ consensus outputs (e.g., consensus

earnings forecasts and consensus recommendations) are the right focal points for investors.

Building on the concept of diversification borrowed from asset pricing, we take into account not

only heterogeneity and persistence in analyst performance, which motivate the literature

contrasting high-quality (HQ; e.g., more accurate, “star”, “All-American”) and low-quality (LQ)

analysts, but also the diversification benefits of relying on the consensus, which can be a first-

order effect.3 Consequently, we advance the literature by considering the market’s focus on

consensus-type information and addressing the question of market pricing and economic efficiency

of consensus outputs. Further, while each of the prior studies examines only one of the outputs of

analysts and only at the firm level, we address our research question based on several outputs—

earnings forecasts, recommendations, and forecast dispersion—at both the individual firm and

market levels, which allows us to reach a general conclusion regarding the phenomenon of

investors’ consensus fixation.

Overall, we find that investors generally focus on the consensus, which leads to price

inefficiency. Differentiating among analysts and following HQ analysts instead of the consensus

can provide economic benefits. Our main results can be summarized as follows: first, the market

3 The literature has found inefficiencies in how the market treats analyst heterogeneity in reacting to earnings forecast

revisions (Stickel, 1992; Clement and Tse, 2003; Gleason and Lee, 2003; Chen, Francis, and Jiang, 2005) and

recommendations (Michaely and Womack, 1999; Mikhail, Walther, and Willis, 2004; Loh and Mian, 2006; Sorescu

and Subrahmanyam, 2006; Ertimur, Sunder, and Sunder, 2007; Fang and Yasuda, 2014; Kucheev, Ruiz, and

Sorensson, 2017).

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reacts to the consensus forecast rather than to the more accurate average forecast generated by HQ

analysts, a categorization based on their past performance. This inefficient use of information in

analysts’ forecasts results in stock mispricing around earnings announcements. Second, we find

that it is not optimal for investors to follow the consensus recommendation revision compared to

the average recommendation revision of HQ analysts. Third, the dispersion of HQ analysts’

forecasts is more informative about the firm’s underlying uncertainty than the dispersion based on

all analysts following the firm (“the consensus dispersion”). Fourth, we find that the post-earnings

announcement drift (PEAD) arises only when the dispersion of HQ analysts is high relative to the

consensus dispersion; thus, investors who do not differentiate among analysts forego significant

returns. Finally, we find that HQ analysts’ recommendation revisions and forecast dispersion

aggregated over all firms in the sample predict the next month’s stock market return and volatility,

respectively, while the corresponding relations are not observed for the consensus

recommendations and consensus forecast dispersion. Taken together, our findings on earnings

announcements, recommendations, forecast dispersion, and the PEAD share an underlying

economic mechanism, which we refer to as the consensus fixation phenomenon, that causes

investors to systematically underweight quality differences among analysts, leading to pricing

inefficiency, and to forego investment returns as a result.

Following the literature (e.g., Chen, Francis, and Jiang, 2005; Loh and Mian, 2006), we

use the firm-year ranking approach and define HQ and LQ analysts according to their forecast

accuracy rankings for the previous year’s annual earnings announcement by the firm. We find

persistence in forecasting ability across time and firms an analyst covers, indicating that

forecasting performance captures analysts’ quality. Next, consistent with the diversification

effect—the more HQ analysts, the smaller the diversification advantage of the consensus relative

to the HQ analysts’ average forecast—we find that the average of HQ analysts’ forecasts is more

accurate than the consensus forecast only when a sufficient number of HQ analysts follow the firm.

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Despite the superiority of the average of HQ analysts’ forecasts for these announcements, the

market reacts more vigorously to earnings surprises that are measured based on the consensus

forecast than the average of HQ analysts’ forecasts. This finding implies that the attention the

market pays to the consensus forecast may be excessive, and investors fail to fully incorporate the

information available in HQ analysts’ forecasts. The market’s fixation on the consensus forecast

is inefficient and can be exploited. A strategy based on the difference between the mean forecast

of HQ analysts and the consensus prior to the earnings announcement day yields economically and

statistically significant abnormal returns over the announcement day and the following trading day.

This phenomenon manifests itself in other aspects of analysts’ informational output, such

as recommendation revisions and forecast dispersion. We find that the market does not efficiently

impound HQ analysts’ recommendation revisions into prices. HQ analysts’ recommendation

revisions are strong predictors of the stock returns in the following month, in contrast to the

consensus recommendation revisions. This results in an opportunity cost for investors who do not

take into account analyst quality heterogeneity and who use investment strategies based on the

consensus recommendation, with a straightforward long-short strategy yielding a 1.1% monthly

alpha. Concerning analysts’ forecast dispersion, if the average of HQ analysts’ forecasts is more

informative than the consensus forecast, then the variability of their forecasts should also be a

superior measure of uncertainty regarding future firm performance relative to the consensus

dispersion. Indeed, we find that the dispersion of HQ analysts’ forecasts is a strong predictor of

the firm’s stock return volatility in the month following the annual earnings announcement month,

unlike the dispersion based on all analysts.

Building on studies showing that the PEAD arises in periods of uncertainty (Abarbanell,

Lanen, and Verrecchia, 1995; Mendenhall, 2004; Zhang, 2006a; Francis et al., 2007; Hung, Li,

and Wang, 2014) and using our finding that HQ analysts’ forecast dispersion can proxy for the

firm’s uncertainty better than the consensus dispersion, we find a significantly greater PEAD

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(9.4% after 11 months) when HQ analysts are relatively uncertain than the PEAD in the full sample

of earnings announcements, which ignores analyst quality heterogeneity. Overall, these findings

indicate that the consensus fixation bias is relevant to both short (e.g., earnings announcements)

and long (the PEAD) investment horizon decisions. Investors recognizing the information

contained in HQ analysts’ forecasts are able to make significantly better investment decisions than

those investors making their investment decisions based on the consensus forecast.

Finally, we examine whether the inferiority of consensus outputs is relevant at the market

level. Since HQ analysts’ recommendation changes are better at the firm level, HQ analysts’

average recommendation change across all firms in the sample can also be a superior predictor of

the market return. We find that HQ analysts’ average recommendation changes predict the market

returns for the following month, in contrast to the consensus recommendation changes. For

example, a long-short strategy based on the direction of HQ analysts’ recommendation revision

relative to the consensus revision produces a 6.8% annualized calendar-time alpha in the month

following the earnings announcement. The argument for the average dispersion of HQ analysts’

forecasts rather than the consensus dispersion predicting market volatility is analogous, and we

find that HQ analysts’ normalized forecast dispersion predicts the next-month CBOE volatility

index (VIX) and changes in the VIX, thereby allowing investors unimpeded by consensus fixation

to earn higher returns.4

Our findings contribute to the literature across several dimensions. First, we analyze the

market efficiency implications of analyst quality differences not previously considered in the

literature. These implications include the short- and long-term reaction to earnings announcements,

4 We also note that aggregating analysts’ informational outputs about firms they follow is akin to surveys aggregating

the opinions of representative households to measure consumer confidence (Ludvigson, 2004), both of which can be

used to predict macroeconomic and market-level variables.

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generating a more informative forecast dispersion measure, and finding the predictability of market

returns and volatility based on the aggregation of analysts’ firm-level outputs.

Second, the study suggests that investors’ focus on the consensus earnings forecast may be

a result of limited attention (e.g., Hirshleifer, Lim, and Teoh, 2009). Investors may prefer the

expediency of the single number of the consensus to the exertion of cognitive effort to assess

analyst quality. From this perspective, our finding that investors ignore the valuable information

contained in HQ analysts’ outputs contributes to the literature that uses subjective expectations of

bond risk premia (Buraschi, Piatti, and Whelan, 2017), corrections for biases in individual

analysts’ forecasts (Chiang et al., 2018), and firm fundamentals (Wahlen and Wieland, 2011; So,

2013) to show that investors can do better than relying on consensus expectations.

The final aspect of our contribution applies to several strands of literature. First, our insight

that different analysts bring different amounts of information to the market advances the debate on

whether recommendations are informative (Barber et al., 2001; Jegadeesh et al., 2004; Altinkilic

and Hansen, 2009; Loh and Stulz, 2011). Second, our findings limit the extent of the PEAD

anomaly’s challenge to market efficiency (Fama, 1998), in that the PEAD is restricted to periods

of high uncertainty regarding the firm’s prospects. Third, our findings on the PEAD and aggregate

volatility suggest that high- and low-uncertainty firms should be identified based on the forecast

dispersion adjusted for analyst quality differences rather than using the consensus-based dispersion

alone (e.g., Diether, Malloy, and Scherbina, 2002; Johnson, 2004; Barron, Stanford, and Yu,

2009).

2. Data and variables

We use the sample of annual earnings per share (EPS) estimates and earnings

announcements in I/B/E/S during January 1992-December 2015 for companies with daily return

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data provided by the Center for Research in Security Prices (CRSP) database.5 The starting year

of 1992 is chosen because some analyses require analysts’ recommendation data, which begin in

1993. The earnings estimates and actual earnings are adjusted for splits using the daily cumulative

adjustment factor from CRSP (Glushkov and Robinson, 2006).

Each year, we rank analysts following the firm based on the closest absolute forecast error,

which is the absolute difference between an analyst’s earnings forecast closest to the earnings

announcement (made at least a day prior to the announcement day) and the actual earnings, divided

by the share price at the beginning of the calendar year. We define HQ (LQ) analysts based on

whether their absolute closest forecast error for the firm-year is below (above) the median absolute

forecast error for the firm-year. The firm-year ranking measure is directly suited for our study

compared to various “star” analyst, cross-firm classifications (e.g., the Wall Street Journal’s “Best

on the Street” or the Thomson Reuters StarMine’s “Top Earnings Estimators”) in that it has the

cross-firm persistence property similar to the star analyst classifications, as we find below, but it

is also simpler (uses only analysts’ prior accuracy in a given firm) and preserves the sample size

because many firms are not followed by such star analysts. In the robustness section, we conduct

sensitivity tests, whose results indicate that our findings are not affected by different cutoff values

or forecast weights in the definitions of HQ and LQ analysts. It is important to note that advancing

the literatures on measuring analysts’ quality, determining the subset of superior analysts, or

analyzing their relative performance is not among our study’s objectives. Instead, we group

analysts by their quality with as simple, realistic, and robust alternative to the consensus, and our

contribution is to examine the economic implications of investors’ ignoring variation in analyst

quality and using the consensus data instead.

5 We focus on annual rather than quarterly earnings for two main reasons. First, fewer analysts provide quarterly

forecasts than annual forecasts. Second, annual earnings announcements are typically more informative, including

that they are more often supplemented with a conference call and followed by recommendation changes.

8

From the initial sample, we generate 861,349 firm-year-analyst rankings based on the

closest forecast error; the number drops to 804,003 observations once we require firms to have

Compustat data. Next, to avoid small sample bias in our ranking when the number of analysts

following the firm is small, we exclude firm-years with fewer than four analysts following, thereby

reducing the sample to 750,295 observations. In addition, for all analyses except those using stock

recommendations (Tables 4 and 8), analysts must appear in the data in two consecutive years for

a given annual announcement to be ranked based on the first of the two years, reducing the sample

to 485,815 observations.

In the firm-level regressions, we control for the following firm characteristics: size, the

annual stock return, the book-to-market ratio, the number of analysts following, and leverage. Firm

size is the market value of the firm’s equity at the end of the month prior to the earnings

announcement month. The annual stock return is measured based on monthly equity returns in the

12 months prior to the earnings announcement month. The book-to-market ratio is computed as

stockholder equity minus preferred stock plus deferred taxes at the end of the fiscal year for which

the earnings are announced and divided by firm size. The number of analysts is the number of

analysts who made at least one earnings forecast for the given announcement. Leverage is the book

value of total liabilities divided by total assets at the end of the fiscal year for which the earnings

are announced. Some of the regression models also control for analyst characteristics: (i) overall

tenure is the number of years since the analyst first appeared in the I/B/E/S file; (ii) firm-specific

tenure is the number of years since the analyst began covering the company in the I/B/E/S file;

(iii) brokerage house size is the number of analysts employed by the brokerage firm; and (iv) firm

coverage is the number of firms covered by the analyst.

In the models predicting market returns and volatility, most of the controls we use follow

Li, Ng, and Swaminathan (2013) and are measured in the month prior to the dependent variable’s

month. The earnings-to-price ratio and dividend-to-price ratio are calculated from the S&P 500

9

dividend, earnings, and price data on Robert Shiller’s website.6 The one-month T-bill rate and 30-

year Treasury yield are obtained from CRSP. The term spread is the difference between the AAA-

rated corporate bond yields obtained from the Federal Reserve Bank of St. Louis (FRED) database

and the one-month T-bill yield. The default spread is the difference between the BAA and AAA

corporate bond yields for the last day of the month when both BAA and AAA daily yields exist,

obtained from the FRED. Inflation is the change in the consumer price index (CPI; all urban

consumers, monthly, non-seasonally adjusted) obtained from the FRED. Following Da, Engelberg,

and Gao (2015), our regressions of the VIX also control for the perceived economic policy

uncertainty (EPU), which is a news-based measure provided by Baker, Bloom, and Davis (2016).

EPU change is the percentage change in the monthly average of the daily EPU for the month prior

to the dependent variable’s month. The VIX is from Wharton Research Data Services (WRDS).

3. Individual analysts

3.1. Sample description and tests of persistence in forecasting performance

Our preliminary analysis determines whether HQ and LQ analysts’ forecast accuracy is

persistent, which is the prerequisite for using groups of analysts ranked according to our quality

measure as alternatives to the consensus. The unit of observation in all analyses in this section is

the individual analyst. Figure 1 shows the mean absolute forecast errors of HQ and all analysts for

each day during the 300 days prior to the earnings announcement. We observe acceleration in the

reduction of the mean forecast error around quarterly earnings announcements at the -90, -180,

and -270 day marks. The graph shows that the mean absolute forecast error of all analysts is higher

than the mean absolute forecast error of HQ analysts in all days prior to the earnings

announcement. This result indicates that the analyst ranking is persistent in the time dimension

6 Available at http://www.econ.yale.edu/~shiller/data.htm.

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because the ranking is based on the previous year’s accuracy. The mean absolute forecast errors

of All and HQ analysts decrease over time to approximately 0.012 and 0.0115, respectively, one

day before the earnings announcement. This difference of 4.17% (0.0115

0.0120− 1) is economically

meaningful and statistically significant (p-value<0.01). Notably, HQ analysts’ accuracy 30 days

before the announcement is already higher than all analysts’ accuracy at the announcement.

Table 1 reports the summary statistics for analysts ranked into the LQ and HQ groups and

examines the persistence of their forecast accuracy. In Panel A, we find that relative to LQ analysts,

HQ analysts tend to be more experienced overall and within individual firms, be employed by

larger brokerage firms, and cover a greater number of firms. To analyze the univariate persistence

of analysts’ forecast accuracy, we compare HQ and LQ analysts’ forecast errors at the earnings

announcement, i.e., a year after they were ranked. The absolute forecast errors of HQ analysts

remain smaller than those of LQ analysts: the difference is 9% (0.0081/0.0089) and statistically

significant. In the last line of Panel A, we find that both HQ and LQ analysts’ forecasts exhibit

approximately equal magnitudes of optimism bias; the average forecast errors are significantly

different from zero, with untabulated p-values<0.01, indicating that HQ analysts’ greater forecast

accuracy does not appear to be associated with a more positive forecast bias (Lim, 2001).

The regression analysis in Panel B of Table 1 examines the persistence in the quality

classification of analysts over time (columns (1)-(4)) and across firms (columns (5) and (6)). In

the probit models in columns (1) and (2), the dependent variable is the HQ status in year t, which

equals one if the analyst is categorized as HQ and zero otherwise. In columns (3) and (4), the

dependent variable is the absolute forecast error, a continuous variable that allows us to control for

firm fixed effects in the regression. In columns (1) and (3), we control for firm characteristics, and

in columns (2) and (4), we control for both firm and analyst characteristics. The main coefficient

of interest is the HQ classification in year t-1. The results show that the coefficient on HQ status

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(t-1) is highly significant (p-value<0.01) in all specifications, indicating that analysts’ rankings

and forecast accuracy are persistent in consecutive years. For example, the unconditional

probability of belonging to the HQ group is approximately 50%, and according to columns (1) and

(2), accounting for the HQ status in the previous year increases this likelihood by approximately

4.1%. Columns (3) and (4) show that HQ analysts continue to have lower absolute forecast errors

in the following year, with their average absolute forecast error being 8.2% lower (0.00072/0.0085)

than the average absolute forecast error for all analysts.

We next conduct cross-firm tests to examine whether forecasting performance is persistent

not only over time but also across firms that the analysts follow. Not only is this analysis important

in its own right, but affirmative findings will also reinforce the argument that some analysts

provide superior information than do others; that is, the HQ designation is not a firm-specific

attribute but, rather, a characteristic of the analyst. We define an analyst’s performance in other

firms as HQ if the analyst is classified in the HQ category for the majority of the other firms that

he or she follows during the year (excluding this firm).7 Columns (5) and (6) of Panel B test

whether ranking as an HQ analyst in the other firms in year t-1 can predict an analyst’s forecasting

performance in year t over and above the HQ classification in year t-1 in the same firm. We

estimate two probit models where the dependent variable is the HQ status indicator in a given firm

in year t. The independent variables of interest are the HQ status indicator of this analyst in the

same firm in year t-1 and the HQ status in other firms indicator, which is equal to one if this analyst

is also HQ in the majority of other firms that he or she followed in year t-1. We find that analysts

who were of HQ in the majority of other firms they followed in year t-1 are 5.1% (p-value<0.01)

more likely to be HQ in a given firm in year t. The coefficient on the firm-specific HQ designation

7 If the number of HQ and LQ rankings of the analyst in the other firms is the same, this analyst-year-firm observation

cannot be categorized as either HQ or LQ in the other firms and is thus excluded from this analysis (approximately

9% of the observations).

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in year t-1 remains positive and significant (p-value<0.01). Hence, the cross-firm findings suggest

that analysts’ forecasting performance transcends across the stocks that they follow and, further,

that HQ analysts are indeed better than their peers in a persistent manner.

3.2. What does persistence in individual forecasting performance mean for the consensus?

Our finding that individual HQ analysts tend to persistently provide more accurate earnings

forecasts than LQ analysts seems to imply that the consensus may be an inferior predictor of future

earnings than the average of HQ analysts’ forecasts. However, the actual extent of how much the

average of HQ analysts’ forecasts is more accurate than the consensus forecast in a specific firm

may depend on the number of HQ analysts following the firm.8 Table 2 empirically investigates

this issue in Panel A and provides statistical tests comparing the absolute standardized unexpected

earnings of consensus (SUE of consensus, equal to the difference between the actual earnings and

the average forecast provided by all analysts following the firm, normalized by the stock price)

with the absolute SUE of HQ analysts, which is based on the difference between the actual earnings

and the HQ analysts’ average forecast.9 We find that as the number of HQ analysts following a

firm increases, HQ analysts as a group eventually become more accurate than the consensus,

confirming our conjecture. Further, when the number of HQ analysts is four or more, the absolute

forecast error of HQ analysts is smaller than the consensus. Therefore, it is in these firms that

8 The intuition is simple—in averaging a greater number of forecasts, the noise portion of their individual forecasts

cancels out more, leading to a more precise forecast of the true earnings signal. The greater the number of HQ

analysts following the firm is, ceteris paribus, the smaller the diversification advantage of the consensus is and more

likely investors are to obtain a more accurate forecast by following the average forecast of the HQ analysts than they

would via the consensus. 9 Because some HQ and LQ analysts may stop covering the firm after year t-1 and new, unranked analysts may

commence coverage, the numbers of HQ and LQ analysts in year t can become too small or too different from each

other (e.g., five HQ and one LQ or vice versa), leading to small sample bias and a lack of robustness when the average

accuracies of HQ, LQ, and all analysts as groups are compared in the firm-level analysis. To mitigate this issue, we

restrict the sample in all firm-level analyses (Tables 2-7) to firm-years in which the numbers of HQ and LQ analysts

are not too different in year t. Specifically, we require that neither of these groups exceeds 75% of all analysts

providing forecasts for a given announcement.

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investors seeking more accurate earnings forecasts should forego the consensus forecast in favor

of the average of HQ analysts’ forecasts. For the same reason, our sample consists of firms with

four or more HQ analysts when we examine whether the market can exploit differential analyst

quality in the analysis of recommendation changes, forecast dispersion, and the PEAD.

In Panel B of Table 2, we report firm characteristics for the samples with fewer than four

and four or more HQ analysts in year t, corresponding to firm-years for which the consensus

forecast is superior or inferior to HQ analysts’ average forecast, respectively. Not unexpectedly,

firms with four or more HQ analysts are significantly larger. While these firms represent less than

50% of all firms, they account for 87% of the market value of the full sample. Firms with four or

more HQ analysts are more levered and perceived by the market to have a greater growth potential

(according to the book-to-market ratio of 0.66, compared to 1.36 for firms with few HQ analysts).

This association between firm characteristics and the number of analysts following (or the number

of HQ analysts) is not surprising and consistent with prior literature. It is important, however, in

the context of our findings, suggesting that the sample for testing the inefficiency of consensus

fixation is not dominated by small firms or firms followed by few or inexperienced analysts.

4. Earnings announcements

The previous section demonstrates that relying on HQ analysts’ earnings forecasts can

generate an earnings forecast that is superior to the consensus forecast. To test whether the market

is aware of this empirical regularity, we examine whether the immediate reaction to the earnings

surprise based on the mean forecast of HQ analysts is greater than the reaction to the earnings

surprise based on the consensus forecast. Table 3 reports the regression results in which the

dependent variable is the buy-and-hold cumulative abnormal return (BHAR) for the earnings

announcement day and the following trading day based on the four-factor model (Fama and

French, 1993; Carhart, 1997). The main variables of interest are the coefficients on the SUE based

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on the consensus and HQ analysts. Table 3 shows that the reaction to the SUE based on the

consensus forecast is greater than the reaction to HQ analysts’ SUE, with a highly statistically

significant difference between the coefficients of 0.103 based on the chi-squared test in the full

sample and a slightly smaller but still highly significant difference of 0.06 in the sample of firms

with four or more HQ analysts. The coefficient on HQ analysts’ SUE is greater and significantly

different from the coefficient on LQ analysts’ SUE, which suggests that the market is partially

aware of the accuracy differences among analysts.10 This finding is in line with Kirk,

Reppenhagen, and Tucker (2014), who show that the market reacts more strongly to the key analyst

than to the least influential analyst following the firm. Importantly, the results indicate that the

market does not sufficiently recognize analyst quality differences because its reaction to the

consensus forecast is significantly stronger even in columns (4)-(6), where HQ analysts are, on

average, more accurate than the consensus.

The finding that the market does not give sufficient weight to HQ analysts’ forecasts

relative to the consensus may have meaningful economic implications. To gauge their magnitude,

we first construct a simple measure of earnings surprise based on the difference between HQ

analysts’ mean forecast and the consensus forecast, labeled predicted surprise. The intuition is to

replace the actual earnings in the SUE formula with HQ analysts’ mean forecast,

𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑠𝑢𝑟𝑝𝑟𝑖𝑠𝑒 =𝐴𝑣𝑔.𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝐻𝑄−𝐴𝑣𝑔.𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑐𝑜𝑛𝑠𝑒𝑛𝑠𝑢𝑠

𝑃𝑟𝑖𝑐𝑒𝑡−1, (1)

so that predicted surprise can be used to predict the SUE of consensus. Investors aware of the

quality differences among analysts would be able to use this measure to predict the immediate

market reaction to earnings announcements. Given that HQ analysts are more accurate than the

consensus and that the market overweights the consensus forecast when it reacts to earnings

10 As a technical note, because the set of analysts covering a firm tends to change after the ranking in the previous

year, the proportion of HQ and LQ analysts varies across firms and years. Therefore, SUE of consensus is not an

average of SUE of HQ and SUE of LQ analysts.

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surprise, one can expect positive or negative abnormal returns to the earnings announcement when

the mean forecast of HQ analysts is greater or smaller than the consensus, respectively. A simple

hedging strategy assessing the predictability of the immediate reaction to earnings announcements

is to buy the stock at the market close on the day before the announcement when the predicted

surprise is positive and to short it when it is negative. Because the market is focused on the

consensus, it will be surprised the most when HQ analysts’ average forecast is different the most

from the consensus. Next, since the consensus includes new analysts, whose quality is currently

unknown because they started to follow the firm after the last year’s ranking, the difference

between HQ and LQ analysts’ forecasts measures analyst heterogeneity not priced because of

consensus fixation. Therefore, we also consider a strategy using an alternative definition for

predicted surprise based on the normalized difference between HQ and LQ analysts’ mean

forecasts:

𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑠𝑢𝑟𝑝𝑟𝑖𝑠𝑒 =𝐴𝑣𝑔.𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝐻𝑄−𝐴𝑣𝑔.𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝐿𝑄

𝑃𝑟𝑖𝑐𝑒𝑡−1 (2)

The potential returns that investors can earn using these alternative predicted surprise measures

represent the returns foregone for investors if they use the surprise based on the difference between

the consensus and actual earnings, thereby not incorporating analysts’ quality differences into

prices.

We report the empirical results in Table 4. The analysis is based on two variations of the

signal based on predicted surprise: the positive predicted surprise and big positive predicted

surprise indicators. Positive predicted surprise is equal to one if predicted surprise is positive and

zero otherwise. A stronger signal, the big positive predicted surprise indicator is one (zero) if

predicted surprise is above (below) the median of its positive (negative) values in the previous

year, and is set to missing otherwise. Using the values of predicted surprise measured in the

previous year ensures that our analysis is out-of-sample. We regress the two-day cumulative

16

BHAR on each of these indicators and control variables. The coefficients on the predicted surprise

indicators are positive and significant in all specifications, reaching 0.0019 in column (3), and the

statistical significance of the predicted surprise indicators is greater for the definition based on the

difference between HQ and LQ analysts’ forecasts. The last line of the table reports the two-day

abnormal returns of a hedging strategy that is long if the predicted surprise indicator of that column

is equal to 1 and short if it is equal to 0. All returns are statistically significant and reach 0.24%

for big positive predicted surprise based on the difference between HQ and LQ analysts’ forecasts.

These returns can be high enough relative to the transaction costs (Novy-Marx and Velikov, 2016)

because predicted surprise achieves its highest values when HQ analysts are most accurate, i.e.,

in firms followed by many analysts (according to Table 2), implying relatively small transaction

costs for these larger firms.

The overall conclusion from Tables 3 and 4 is that the market seems to overreact to the

actual earnings’ deviations from the consensus, compared to deviations from HQ analysts’ average

estimate. This fixation on the consensus forecast presents an opportunity cost for investors and

prevents stock prices from efficiently reflecting the available information.

5. Stock recommendations, forecast dispersion, and implications for the PEAD

The persistence in analysts’ forecasting performance over time and across stocks suggests

that HQ analysts have superior ability; thus, it is possible that they issue superior stock

recommendations compared to the consensus recommendation based on all recommendations for

the firm.11 Further, given that HQ analysts are better at forecasting future earnings, the dispersion

in their forecasts is likely to contain more relevant information than the dispersion of the forecasts

11 A relation between earnings forecasts and recommendations has been examined in the prior literature (e.g., Francis

and Soffer, 1997; Bradshaw, 2004; Loh and Mian, 2006; Ertimur, Sunder, and Sunder, 2007).

17

of the entire set of analysts following the firm. In this section, we empirically examine these

predictions.

5.1. Stock recommendations

To gauge whether investors can benefit from being aware of the differences in analysts’

forecasting ability, we examine how future returns are associated with the recommendation

revisions of different subsets of analysts. If investors internalize and act on the quality differences

among analysts, which would imply that they are not fixated on the consensus recommendation,

then no relation between future returns and recommendation revisions should obtain regardless of

the quality of the analysts making the recommendations.

A recommendation is an integer between 1 and 5, where 1 is “strong buy”, 5 is “strong

sell”, and 3 is “hold”. For ease of interpretation, we measure recommendation revisions as the

negative of the current recommendation of the analyst minus the previous recommendation of the

analyst; thus, a positive recommendation revision is an upgrade. The recommendation revision for

the firm is the average of individual analysts’ revisions. The sample consists of the

recommendation revisions made during the month of the annual earnings announcement. The

earnings announcement month has several advantages making it the best time frame to examine

whether the market efficiently incorporates its knowledge of analyst quality into its reaction to

recommendations. First, the month with the annual announcement has the most information for

analysts to process during the year because the information in earnings announcements has a major

influence on recommendation revisions (Yezegel, 2015). Second, analysts of different quality

types face the same information set when making recommendations that month, in contrast to

recommendations at random dates during the year. Finally, and perhaps most importantly, it is the

earnings announcement month that reveals that the market is fixated on the consensus forecast and

18

does not recognize superior HQ analysts; thus, we expect this pattern to be prominent for HQ

analysts’ stock recommendations during this month, as well.

We first examine the immediate market reaction to recommendation revisions, which is

inherently an individual analyst-level rather than analyst group-level event, i.e., there is no

consensus recommendation to consider in the analysis of the immediate reaction. The untabulated

regressions of the immediate market reaction to HQ and LQ analysts’ individual recommendation

revisions yield results that are consistent with the finding for earnings announcements: investors

recognize, at least to an extent, the more accurate forecasters by reacting more strongly to the

recommendation revisions of HQ analysts relative to those of LQ analysts. However, the important

question remains whether the market fully incorporates quality differences into prices or is fixated

on the consensus recommendation.

Table 5 reports the results concerning a delayed response to recommendation revisions by

different analyst types. For each calendar month with an annual earnings announcement by a given

firm, we average all, HQ, and LQ analysts’ recommendation revisions and regress the next months’

stock return on these recommendation revision averages. This analysis predicting equity returns

one calendar month ahead enables us to use all revisions during the current month because, by the

end of that month, investors have learned and updated the analyst quality classification based on

this new earnings announcement.12 The investment delay from the revision date to the end of the

revision month provides investors with sufficient time to react to the revision and, because such a

12 The updated analyst ranking also allows all the revisions to be used because all analysts following the firm are

ranked as of the end of the announcement month, i.e., there are no revisions by unranked, newcomer analysts who

have just started following the firm between the earnings announcement and the end of the month. The sample has

exactly 50% HQ and 50% LQ analysts; thus, the requirement for earnings announcements that at most 75% of forecasts

are made by one analyst type is not binding for recommendation revision analyses.

19

delay reduces the market response the next month, leads to conservative return estimates for the

next month (Barber et al., 2001).13

The regression results in columns (1)-(3) of Table 5 reveal that the coefficients on the

consensus and HQ recommendation revisions are positive and significant. The greater coefficient

for HQ analysts and not significant coefficient for LQ analysts imply that price momentum

following consensus recommendation revisions (e.g., Jegadeesh et al., 2004) is driven by HQ

analysts’ recommendation revisions.14 This supports the argument in the literature that analyst

recommendations bring new information to the market (Jegadeesh et al., 2004; Loh and Stulz,

2011).

To examine whether investors should follow the HQ recommendation revision rather than

the consensus recommendation revision, we regress the next month’s return on the difference

between HQ analysts’ and consensus recommendation revisions. The intuition for this test is that

the gain for investors is the greatest when HQ analysts are relatively more informed, i.e., when

their average recommendation is more different from the consensus recommendation. The

regression result in column (4) shows that following HQ analysts’ upgrades or downgrades net of

the consensus revision leads to higher out-of-sample returns for investors.

To further assess the additional value inherent in incorporating analyst quality differences

into investment decisions, we examine the returns of a long-minus-short strategy in the month

following the revisions, where the long (short) position is in the firms for which the consensus,

HQ, LQ, or HQ minus the consensus mean recommendation revision variable is positive (negative)

during the earnings announcement month. The last two lines of Table 5 report both the event-time

13 The results for predicted monthly returns in Table 5 are unaffected by using the subsamples of recommendation

revisions made either before or after the earnings announcement during that calendar month or coinciding with the

announcement’s two-day window. We also reach the same outcome by conducting event-time analysis using returns

over the periods (2,32) and (2,62) days following the revision. 14 Loh and Mian (2006) and Ertimur, Sunder, and Sunder (2007) contrast market responses to the recommendations

of more and less accurate analysts based on a partially contemporaneous rather than predictive relation between the

recommendations of the two quality groups and stock returns.

20

average long-short return and the four-factor alpha based on the calendar-time approach for this

strategy. In particular, with HQ analysts’ recommendation revisions, the resulting one-month

strategy return is 0.85% and highly statistically significant, in contrast to the consensus

recommendation revisions, for which the hedging strategy yields a statistically nonsignificant

0.36%. For the HQ net of the consensus trading signal, the return is even higher, at 1.24% per

month. The calendar-time approach finds that investors achieve a significant alpha of 1.06%

(12.72% annualized) when they rely on HQ analysts’ recommendation revision net of the

consensus recommendation revision.

Overall, the predictive relation between analyst recommendation revisions and equity

returns in the subsequent month is driven by HQ analysts’ mean recommendation rather than the

consensus recommendation. Hence, our findings suggest that analyst quality based on earnings

forecasts generalizes to recommendation revisions and that investors can earn significant

additional returns by taking into account analyst quality differences instead of relying on the

consensus recommendation. These conclusions are entirely consistent with the notion that treating

all analysts as equal and, thus, using the consensus measure of analyst output can lead to inefficient

pricing.

5.2. Analysts’ forecast dispersion and volatility

Analysts’ forecast dispersion has been widely used as a proxy for uncertainty about firms’

future prospects. We conjecture that just as HQ analysts’ superior earnings forecasts and

recommendations indicate that they have superior information concerning firm value, these

analysts’ forecast dispersion similarly contains more accurate information about future

uncertainty. We examine whether the disagreement about the firm’s prospects among HQ analysts

is a superior predictor of uncertainty surrounding the firm’s future performance, measured by

21

future return volatility, relative to the disagreement among all analysts, which we call the

consensus dispersion.

Table 6 reports the results of regressing stock return volatility during the month following

the earnings announcement month on the standard deviation of analysts’ forecasts before the

earnings announcement. To avoid stale forecasts and to make forecasts more comparable in terms

of their proximity to the announcement, we use only the forecasts in the 60 days prior to the

announcement.15 We consider the dispersion of forecasts by all, HQ, and LQ analysts separately,

whose coefficients are the variables of interest. HQ analysts’ forecast dispersion is statistically

significant, while the consensus dispersion is not significant. These findings suggest that only HQ

analysts’ forecasts capture variation in uncertainty, which is associated with future equity volatility

in a given firm. This result extends the earlier findings of a contemporaneous relation between

analysts’ forecast dispersion, stock volatility, and the option value of the firm (Ajinkya and Gift,

1985). The next two subsections illustrate how investors can benefit from utilizing HQ analysts’

dispersion instead of the consensus dispersion.

5.3. Post-earnings announcement drift

Our results concerning the differences in the properties of forecast dispersion of all and

HQ analysts’ forecasts have important implications for the PEAD anomaly. First, the model

proposed by Abarbanell, Lanen, and Verrecchia (1995) predicts that when forecast dispersion is

high, investors place less weight on the forecasts relative to their private information, so that

investors reduce their immediate response to earnings surprise. Consequently, following the

15 The length of the measurement period for forecast dispersion significantly varies in the literature. For instance, it

can be one month (Krishnaswami and Subramaniam, 1999), four months (Zhang, 2006b), six months (Babenko,

Tserlukevich, and Vedrashko, 2012), and up to one year since the previous earnings announcement (Diether, Malloy,

and Scherbina, 2002). Our choice of 60 days ensures that we use only the annual earnings forecasts made after the

previous quarterly earnings announcement. Our results are unaffected by using a different period length.

22

announcement, as investors receive more information over time, prices adjust in a manner

potentially resulting in a PEAD. Similarly, Zhang (2006a) argues that investor underreaction to

public information is more significant when uncertainty is high and finds that analysts’ forecast

dispersion predicts a price drift following analysts’ forecasts.16 Second, our finding of a relation

between HQ analysts’ dispersion and return volatility, combined with a relation between return

volatility and the PEAD documented in Mendenhall (2004), posit a link between HQ analysts’

dispersion and the PEAD. For the full set of analysts, this relation is expected to be weaker because

of a weaker relation between consensus dispersion and return volatility.

Therefore, we examine whether investors can better exploit the PEAD when the dispersion

of HQ analysts’ forecasts is high and relative to the consensus dispersion than when they disregard

analyst quality differences.17 We calculate the PEAD using the calendar-time approach. To be able

to relate our results to the PEAD literature, we use the consensus earnings surprise measure to

assign announcing stocks to a long or short portfolio at the end of each month, depending on

whether the earnings surprise (SUE of consensus) is positive or negative, respectively. The stocks

are then held in the two portfolios for horizons from 1 to 11 months to avoid overlapping with the

next annual earnings announcement. The monthly PEAD is the alpha from regressing the monthly

value-weighted portfolio returns on the four Fama-French and Carhart factors.18 The cumulative

PEAD is the monthly alpha for a given horizon (the number of months that the stock is held in the

16 In related studies, Francis et al. (2007) find a positive relation between uncertainty, which they measure with the

unexplained portion of working capital accruals, and the PEAD. Hung, Li, and Wang (2014) find that exogenously

reduced information uncertainty leads to a lower PEAD. 17 For an association between the PEAD and HQ analysts’ forecast dispersion to exist, investors do not need to be

aware or take into account HQ analysts’ forecast dispersion because they can learn about the firm’s uncertainty level,

including its systematic component, from a variety of sources. HQ analysts’ forecast dispersion effectively reflects

that information. 18 We obtain similar results using equal-weighted portfolios. Separately, we also note that because of our sample’s

requirement that four or more HQ analysts follow the firm, the sample consists of relatively large firms, thereby

reducing the likelihood that any findings may be attributed to illiquidity (Sadka, 2006).

23

long or short calendar-time portfolio) multiplied by the horizon length in months. The resulting

relation between forecast dispersion and the PEAD is presented in Figure 2 and Table 7.

Figure 2 reports the cumulative long PEAD portfolio return minus the short PEAD

portfolio return for the sample of announcements with high uncertainty, defined as announcements

for which HQ analysts’ forecast dispersion is greater than the consensus dispersion, the low-

uncertainty sample, in which HQ analysts’ forecast dispersion is lower than the consensus

dispersion, and the full-sample, i.e., regular, PEAD. The high-uncertainty PEAD is clearly greater

than the full-sample PEAD, and the low-uncertainty PEAD is below the full-sample PEAD. The

largest cumulative long-short abnormal return of the PEAD strategy is 11.2%, reached eight

months following high-uncertainty announcements. Table 7 reports the monthly alphas on long,

short, and long-minus-short strategies for the subsamples with high- and low-uncertainty

announcements. We find that the low-uncertainty PEAD alpha (approximately 60% of the

announcements) is not statistically significant except for the 11-month horizon. In contrast, when

the forecast dispersion of HQ analysts is greater than the consensus dispersion, the abnormal return

of the long-minus-short portfolio is highly statistically significant at almost all horizons. To

determine the additional return that investors can earn from this strategy over and above the return

from the simple PEAD strategy, we regress the long-short post-announcement raw return for the

high-uncertainty portfolio on the four Fama-French and Carhart factors and the long-short post-

announcement raw return for the portfolio including all announcements. The resulting monthly

alphas for different horizons are reported in column (7). Investors can earn up to 9.4% cumulative

alpha (at the eight-month horizon) over and above the regular PEAD alpha. Overall, the PEAD is

observed primarily during periods of high information uncertainty, as determined by the forecast

dispersions of HQ analysts, which allows investors who are not fixated on the consensus forecast

and recognize analyst quality differences to achieve better investment performance.

24

6. The content of HQ analysts’ information output at the aggregate

Our findings that HQ analysts’ have superior ability to forecast earnings, issue more

informative recommendations, and have better forecasts of volatility have immediate implications

for aggregate returns and volatility: we should expect that the superior abilities at the firm level

manifest themselves at the aggregate market levels, thereby benefiting investors who overcome

their consensus fixation. Accordingly, we average the changes in recommendations of all, HQ, and

LQ analysts across all firms that made an annual earnings announcement this month and examine

whether the consensus or HQ analysts’ average recommendation revisions predict future market

returns. The aggregation argument works similarly for forecast dispersion, in that aggregating HQ

analysts’ dispersion across all firms in the sample should result in a dispersion measure reflecting

the degree of uncertainty in the market.19

In Table 8, Panel A, we report the estimation results for the relation between revisions in

stock recommendations and future market returns. To that end, each month, we calculate a simple

average of HQ, LQ, and all analysts’ recommendation changes across all firms that announce

annual earnings, resulting in one monthly time series for the average recommendation change in

the market. The dependent variable is the value-weighted market return in the month following the

recommendation change month. The consensus mean recommendation revision is the mean of all

recommendation changes during the month in which the firm's earnings are announced. The HQ

(LQ) mean recommendation revision is an analogous variable that is based only on

recommendation changes of HQ (LQ) analysts. The HQ-consensus mean recommendation

revision is equal to the difference between the HQ analysts’ and consensus mean recommendation

revisions when the HQ analysts’ mean revision is either positive and greater or negative and

19 Notably, the aggregation principle does not assume and the aggregate findings do not indicate that individual HQ

analysts have superior macroeconomic knowledge or ability to predict market-level developments (e.g., Hutton, Lee,

and Shu, 2012).

25

smaller than the consensus revision; otherwise, this variable is zero. The control variables follow

Li, Ng, and Swaminathan (2013) and also include the previous month’s market return to account

for return momentum.

The regression results reveal that the coefficient on the consensus recommendation revision

is positive and weakly statistically significant, indicating that the information in recommendation

revisions is not fully internalized by the market. However, this coefficient’s significance is entirely

due to the mean recommendation revision by all HQ analysts because LQ analysts’ coefficient is

not statistically significant. The coefficients on the HQ revision net of the consensus revision in

columns (4) and (8) are greater than the other coefficients, suggesting that when HQ analysts are

comparatively more informed and, thus, their recommendations deviate more from the consensus,

investors can benefit more from following the mean of HQ analysts’ recommendation revisions.

To estimate the economic magnitude of this market return predictability, we conduct an out-of-

sample trading strategy analysis, reported in the last line of Panel A. The long and short trading

signals are based on the historical variation in monthly mean recommendation changes as follows:

if the average recommendation revision for a given month is greater (smaller) than the median of

the monthly average recommendation revisions over the previous 24 months, i.e., the current

recommendation revision is more optimistic (pessimistic) than they were in the recent past,

investors should buy (short) the market value-weighted index and hold it for one month.20 For the

variable based on the difference between HQ and consensus mean recommendation revisions in

the last column of Panel A, one should buy (short) the market when this variable is positive

(negative), i.e., when HQ analysts, on average, upgrade and are more optimistic (downgrade and

are more pessimistic) than the consensus mean revision. We benchmark the performance of these

20 The results are unaffected by selecting a longer historical window of up to five years. The 24-month window that

we use minimizes the number of months lost to initialize this out-of-sample analysis, while providing enough

observations to robustly calculate the median of monthly mean recommendation changes.

26

strategies against the market return and report the market model alphas. Only HQ analysts’

recommendations produce statistically significant alphas, with a particularly large alpha based on

HQ analysts’ mean recommendation when it is different from the consensus recommendation, at

0.57% per month (6.84% annualized). These findings suggest that investors can earn economically

meaningful returns if they follow the recommendations of a subset of HQ analysts and not the

consensus recommendation.

In Panel B of Table 8, we examine another market-level aggregate relation—whether HQ

analysts’ forecast dispersion aggregated across all firms is associated with systematic uncertainty

in the economy captured by current or future market volatility. We use the VIX to measure

expected market volatility. To capture the degree to which HQ analysts’ uncertainty is different

from the consensus (all analysts’) uncertainty, we define the dispersion ratio for HQ analysts as

the HQ analysts’ forecast dispersion divided by the forecast dispersion of all analysts following

the firm. The dispersion ratios are analogous to the measures of uncertainty in the PEAD analysis.

A bonus feature of HQ and LQ analysts’ forecast dispersions being normalized in the dispersion

ratios is that they are made comparable across firms and years and can thus be suitably aggregated

to measure market uncertainty. A market-level measure of analyst uncertainty is created by firm

value-weighting the dispersion ratios across firms each month, and we also include the results for

aggregate dispersions for completeness.

Panel B reports the regressions of monthly VIX returns (this month’s VIX divided by the

last month’s VIX, minus one) on the dispersions of all, HQ, and LQ analysts’ forecasts and the

HQ and LQ analysts’ dispersion ratios measured before the earnings announcement in the previous

month.21 The results indicate that a higher dispersion ratio for HQ analysts predicts a greater VIX

return in the following month. The LQ dispersion ratio does not capture the level of uncertainty in

21 We also obtain very similar results using the VIX values in lieu of the returns.

27

the market, nor do the non-normalized forecast dispersion variables. To estimate the opportunity

cost for investors not recognizing the limitation of relying on the consensus forecast dispersion,

the last line of Panel B reports the performance of a long-short strategy for the VIX identical in

design to the long-short strategy for the recommendations market return index. If the forecast

dispersion measure in the corresponding column in a given month is above the median of its

monthly values during the previous 24 months, then the strategy is to long the VIX return in the

next month. If the forecast dispersion measure is below the median, then the VIX return is shorted.

To benchmark the performance of these monthly strategy return series, we regress it on the market

return and report the alphas. The only statistically significant (p-value<0.01) abnormal return is

for the trading signal based on HQ analysts’ dispersion ratio; the strategy yields an economically

significant return of 3.32% per month.22 We conclude that when HQ analysts are, on average, more

uncertain than other analysts about the prospects of the firms they follow, investors should expect

an increase in market-wide uncertainty.

Together, consistent with the firm-level findings, the aggregate results indicate that the

market’s fixation on the consensus recommendation and the consensus forecast dispersion results

in a delayed incorporation of information into prices, both at the individual firm level and at the

market level. Investors who recognize quality differences among analysts can benefit from

exploiting this market inefficiency.

7. The definition of high-quality analysts

22 While this alpha is much higher than the typical alphas for stock-based long-short strategies, it is credible because

the market may not be able to fully arbitrage it away. The transaction costs of implementing a VIX strategy with

complete end-of-month rebalancing using VIX futures would be much higher than transaction costs for stocks because

of a significant contango in the VIX futures market, resulting in costs of approximately 14% per month (Nadig, 2016).

Further, the VIX strategy’s average monthly raw return and volatility are 2.3% and 19.6%, respectively.

28

Based on the combined findings of sections 4-6, we reject the null of the economic

efficiency of consensus fixation using a simple measure of analyst quality differences. In this

section, our robustness analysis examines the sensitivity of our finding of the inefficiency of

consensus fixation to the definition of HQ analysts. The firm-year definition used throughout this

paper, which splits analysts into two groups at the median based on the accuracy of their closest

estimate to the annual EPS announcement, is only one of many ways of ranking analysts and

generating an alternative to the consensus forecast. A ranking that, like ours, is based on the last

year’s forecast accuracy is used, for instance, in Loh and Mian (2006) and supported by Sinha,

Brown, and Das (1997), who find it to be superior to rankings based on more years, and Carpenter

and Lynch (1999), who find it to be relatively less exposed to survivorship bias.23 Other ranking

methods can include such variations as using different forecast accuracy cutoffs between the two

groups and giving different weights to forecasts.24 We note that our analysis of the inefficiency of

consensus fixation does not require finding the subset of analysts who beat the consensus by the

23 More generally, rankings based on past performance are common for analyst forecast persistence studies (Stickel,

1992; Sinha, Brown, and Das, 1997) and in a number of other areas, such as the mutual fund and pension fund

performance forecasting (Hendricks, Patel, and Zeckhauser, 1993; Carhart, 1997; Tonks, 2005) and economic

forecasting (Aiolfi and Timmerman, 2006) literatures. Brown (2004) finds that models built on past forecasting

performance predict analysts’ forecasting accuracy as well as a model based on analysts’ individual characteristics,

such as that in Clement (1999). 24 A somewhat more different approach is to rank analysts in a given year by averaging their forecast errors across the

firms they follow. This method underlies various “star” analyst rankings, which are cross-firm by design. This

alternative ranking procedure would avoid losing the observation of the first year when an analyst begins covering a

firm, as we could use the analyst’s ranking in other firms. However, the cross-firm ranking approach has several

pitfalls. First, an aggregated ranking across firms can be misleading if an analyst’s superiority is mainly firm- or

industry-specific (e.g., Kadan et al., 2012). Second, with the cross-firm ranking, we end up with some firms followed

almost exclusively by either HQ or LQ analysts and even populated by just one analyst quality type, coinciding with

the consensus, which would undermine our study’s objective because it relies on comparing the average outputs of

different analyst types to the consensus in each firm. While the cross-firm ranking approach is not suitable for this

study, its ranking characteristics are effectively provided by our firm-year ranking measure: Table 1 shows that an

analyst’s forecast accuracy in a given firm and the accuracy measure based on all firms covered by the analyst are

highly correlated.

29

greatest margin or whose other outputs result in the greatest additional returns relative to the

returns based on the consensus measure.25

The first two alternative ranking procedures that we consider in this section define HQ

analysts as those in the top 70% (with the HQ/LQ proportion at 70%/30%) and the top 30% (with

the HQ/LQ proportion at 30%/70%) of forecast accuracy distribution. Appendix A examines a

broad range of possible cutoff values for HQ analysts and finds that analyst forecasting

performance is persistent over time for all cutoffs. The third alternative definition for HQ and LQ

analysts is computed using all forecasts, rather than the most recent forecast, and gives different

weights to forecasts, depending on how long the forecast has been outstanding. The details of this

time-weighted analyst quality measure are also provided in Appendix A.

Next, we repeat the key firm-level analyses of the paper with the three alternative quality

definitions. If HQ is defined as the top 70% of analysts, then the smallest number of HQ analysts

following the firm is three for their average forecast accuracy to be superior to the consensus

forecast. In that subsample, the market reaction to the consensus forecast is greater than that for

HQ analysts. Importantly, the market does not sufficiently recognize analyst quality differences

and is fixated on the consensus forecast, resulting in predictable mispricing at the earnings

announcement day. These results for forecasts are also robust to defining the top 30% of analysts

as HQ. The results on return and volatility predictability for recommendations and forecast

dispersion are little affected by the first two alternative definitions.26 With the time-weighted

analyst quality definition, HQ analysts’ average forecast is more accurate than the consensus when

four or more analysts follow the firm. The design of the time-weighted measure results in a

25 For these reasons, this study is not related to a literature in economics and statistics aiming to achieve better

forecasting performance than the consensus forecast by proposing different methods of combining forecasts (e.g.,

Conroy and Harris, 1987; Clemen, 1989; Brown, Gay, and Turac, 2008). 26 For HQ defined as the most accurate 70% of analysts, firms with three or more HQ analysts constitute approximately

2/3 of all firms, indicating that our findings about the inefficiency of consensus fixation are not limited to large firms.

30

relatively small sample size, which could explain that while the market reacts more to the

consensus than to the average of HQ analysts’ forecasts based on this measure, this difference is

not statistically significant. However, this result does not mean that the market sufficiently

recognizes analyst quality differences because it would then react more strongly to the average of

HQ forecasts than it would to the consensus. The replication results of the other tables hold for the

time-weighted quality measure as consistently as for the first two alternative cutoff measures.

Overall, we conclude that the definition of HQ analysts and the smallest required number of HQ

analysts associated with this definition are immaterial for our conclusion about the inefficiency of

consensus fixation. More generally, any alternative to the consensus forecast can work for this

analysis as long as it is more accurate than the consensus forecast.

8. Conclusion

Investors can benefit from disregarding the consensus and using a signal with greater

information content. However, the market does not demonstrate an appropriate awareness of these

significant deficiencies in the consensus: the market reacts more strongly to deviations from the

consensus earnings forecast than it does to deviations from HQ analysts’ forecasts. In addition,

HQ analysts’ stock recommendations and forecast dispersion predict the first two moments of firm

and stock market returns better than the corresponding consensus recommendation and forecast

dispersion of all analysts. In short, the persistence of analysts’ differential ability along multitude

dimensions is not sufficiently recognized by the market, resulting in inefficient pricing after

earnings announcements and stock recommendations changes. Overall, our findings suggest that

the market’s fixation on the consensus forecast is not justified. The forecasts and other information

outputs of HQ analysts demonstrably provide superior, more accurate information than the

consensus figures.

31

We show that sell-side research analysts’ superior forecasting ability is reflected not only

in individual stocks but also at the aggregate market level. This result is particularly surprising, as

the limits to arbitrage are much narrower at that level because the aggregate stock market is much

more liquid than individual stocks. This finding implies that the fixation on the consensus is not

limited to individual investors but affects institutional investors, as well. This conclusion is

corroborated by our finding that firms with a greater number of HQ analysts are larger and have

greater analyst following, which are associated with greater institutional holdings. Consequently,

the question arises whether investors’ fixation on the consensus can be remedied. Tracking analyst

performance by the investing public is a necessary step towards this objective. News and

information provider outlets, both electronic and non-electronic, can also play a major role in this

regard by changing how they report and present data on analysts’ expectations to help investors

circumvent their cognitive constraints and fully take into account the variation in analyst quality.

32

Appendix A

The appendix provides details on how several alternative classifications of analysts into

the HQ and LQ groups affect the persistence in analyst forecasting performance. The ranking

procedure sorts analysts in a given firm-year based on their absolute forecast error. In general, HQ

analysts are those who are ranked in the top 𝑝 percent of analysts, while LQ analysts are those in

the bottom (1 − 𝑝) percent. If analysts’ forecasting performance were uncorrelated across years,

then the fractions of analysts who preserve their ranking in two consecutive years as HQ and LQ

would be 𝑝2 and (1 − 𝑝)2, respectively, or 𝑝2 + (1 − 𝑝)2 of all analysts.

Figure A.1 plots the fraction of analysts who retain their rankings in consecutive years and

the expected fraction assuming no performance correlation across years. In this figure, to rank

analysts up to the decile on the horizontal axis, the sample is constrained to firms that are followed

by ten or more analysts. We find that with all cutoff values of 𝑝 on the horizontal axis, the actual

fraction of persistent forecasting performance is above the expected fraction and that all the

differences are statistically significant (p-value<0.01). For example, when we classify the top 10%

of analysts following a firm in a given year as HQ (p=10%) and the bottom 90% as LQ, the

expected fraction given random assignment is 0.92 + 0.12 = 0.82. The figure shows that the

actual fraction is greater than that at 0.843. The overall finding is that for all of the cutoff values,

there is a sizeable persistent component; thus, for accuracy persistence, which exact cutoff value

we choose to partition HQ and LQ analysts should make little difference.

The two alternative cutoffs for HQ analysts—the top 70% (so that the LQ analysts are the

bottom 30%) of analysts and the top 30% (the LQ analysts are the bottom 70%) of analysts, which

are considered in Section 7—are symmetric around the cutoff at the median used throughout this

paper. Because analysts are ranked in year t-1, the proportion of HQ and LQ analysts following

the firm tends to become different at the year t announcement, potentially resulting in too few HQ

or LQ analysts for the firm. To avoid small sample bias, these alternative analyst quality definitions

33

require the same restrictions on the sample as those used in the rest of this paper, with an additional

condition. For the robustness analysis, we require that the proportion of HQ and LQ analysts does

not change by more than a 20% margin from t-1 to t. The motivation is obvious: for the definition

of HQ analysts as the top 30% in year t-1, the additional condition ensures that their fraction always

stays above 10% of analysts covering the firm in year t; and if HQ analysts are defined as the top

70% in year t-1, then their fraction can be between 50% and 90% of analysts in year t, while the

fraction of LQ analysts never falls below 10% of analysts covering the firm in year t.

The third ranking is based on the time-weighted absolute forecast error, which is computed

using all forecasts by the analyst during the 300 days prior to the annual earnings announcement.

This measure is similar to the time-weighted bid-ask spread that is commonly used in the market

microstructure literature (e.g., McInish and Wood, 1992; Lee, Mucklow, and Ready, 1993;

Bessembinder, 1999; Rubin, 2007). For a given announcement and analyst, it is computed as

follows:

𝑇𝑊𝐹𝐸𝑡 =𝐹𝐸300×𝑑1+∑ (𝐹𝐸𝑗×𝑑𝑗)𝑛

𝑗=2

300 (3)

where 𝑇𝑊𝐹𝐸𝑡 is the time-weighted absolute forecast error of the analyst in year t; 𝐹𝐸300 is the

absolute forecast error based on the forecast outstanding on the 300th day prior to the earnings

announcement; 𝑑1 is the number of days that this forecast is outstanding (from the 300th day prior

to the earnings announcement to the earliest of the earnings announcement day or the following

earnings forecast revision day); n-1 is the number of estimates issued by the analyst between the

299th day prior to the earnings announcement and the earnings announcement day; 𝐹𝐸𝑗 is the

absolute forecast error of forecast j; and 𝑑𝑗 is the number of days that the forecast has been

outstanding. The advantage of the time-weighted measure is that it captures the analyst’s ability

over a four-quarter period, instead of at a single point just before the annual earnings

announcement. However, the measure’s disadvantage is that it excludes analysts who have not

34

provided an annual forecast 300 or more days prior to the annual earnings announcement day. The

sample therefore shrinks by approximately 65% relative to the sample used throughout this paper,

thus both reducing the power of our empirical analysis with this quality measure and possibly

biasing the results because it remains unknown whether the lack of early forecasts is due to the

analyst’s poor ability or a neutral reason, such as common practice in the given industry or firm

being analyzed. These disadvantages are among the reasons the analyst classification used in our

paper equal-weights the forecasts made by the best performing subset of analysts, which is

certainly more common in the literature and analogous to the approach examined, for instance, in

Aiolfi and Timmerman (2006). Further, studies focused on the forecast weighting topic find that

the simple averaging of expert forecasts is commonly equivalent or more optimal than more

sophisticated weighting methods for various economic series (Genre et al., 2013).

35

Figure A.1: Persistence in analysts’ forecasting performance. This figure depicts how the fraction of

analysts retaining their ranking of either high- or low-quality (HQ and LQ) in terms of forecast accuracy in

two consecutive years depends on the cutoff percentile in the definition of HQ analysts. HQ analysts are

those whose closest absolute forecast errors are less than the absolute forecast error at the cutoff percentile

(the horizontal axis) of the distribution of forecast errors for the firm’s annual earnings announcement in

year t-1. The closest absolute forecast error is the absolute difference between an analyst’s forecast estimate

closest to the earnings announcement prior to the announcement day and the actual annual earnings, divided

by the share price at the beginning of the calendar year. Expected performance assuming no persistence is

the fraction of analysts who would have the same forecast performance category in two consecutive years

if their performance were uncorrelated between years.

45%

50%

55%

60%

65%

70%

75%

80%

85%

90%

10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90%

Perc

enta

ge o

f analy

sts

with t

he s

am

e q

ualit

y cate

gory

in t

wo c

onsecutive

years

Percentage of analysts defined as HQ

Expected performance (assuming no persistence) Actual performance

36

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Figure 1: Absolute forecast errors up to 300 days before the annual earnings announcement day. The absolute forecast error is the absolute

difference between an analyst’s forecast estimate and the actual annual earnings, divided by the share price at the beginning of the calendar year. The absolute forecast error at day -t prior to the earnings announcement date is calculated as the mean absolute forecast error based on all annual

earnings forecasts outstanding for the firm as of that day, averaged across the firm’s announcements and then averaged across firms. HQ analysts

are those whose closest absolute forecast errors are below the median closest absolute forecast error for the earnings announcement in the previous

year, where the closest absolute forecast error is that closest to the announcement day prior to that day.

0.010

0.011

0.012

0.013

0.014

0.015

0.016

0.017

0.018

0.019

0.020

0.021

0.022

0.023

0.024

0.025

0.026

0.027

-300 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0

Mean

ab

so

lute

fo

recast

err

or

Days before earnings announcement

All analysts High quality analysts

42

Figure 2: Cumulative post-announcement drifts and analysts’ uncertainty This figure shows the cumulative returns for 1- to 11-month horizons following earnings announcements. Each month, stocks enter a calendar-time

long (short) portfolio, depending on whether their earnings surprise is positive (negative), where earnings surprise is defined based on the consensus

estimate in Table 2. The horizontal axis is the drift’s horizon, which is the number of months a stock is held in the calendar-time portfolio. The

monthly long-minus-short value-weighted portfolio return is regressed on the four Fama-French-Carhart factors. The cumulative drift for a given

drift horizon on the vertical axis is calculated as the regression intercept (monthly alpha) multiplied by the portfolio’s horizon length in months. The

graphs are shown for the full sample and two subsamples of firms in which the standard deviation of HQ analysts’ forecasts (SD HQ) is either greater

or smaller than that of all analysts’ forecasts (SD consensus) for the firm-year. Analysts are ranked as HQ based on their previous year’s absolute

forecast errors, defined in Table 1.

-4

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 10 11

Cum

ula

tive r

etu

rn (

%)

Horizon (months)

Full sample SD HQ > SD consensus SD HQ < SD consensus

43

Table 1: Individual analyst analysis: characteristics and persistence of forecast accuracy Panel A conducts univariate analysis for high- and low-quality (HQ and LQ) analysts. HQ (LQ) quality analysts are those

whose closest absolute forecast errors are below (at or above) the median closest absolute forecast error for the firm’s

earnings announcement. The closest absolute forecast error for an analyst is the absolute difference between the analyst’s

forecast closest to the earnings announcement prior to the announcement day and the actual annual earnings, divided by

the share price at the beginning of the calendar year. Overall tenure is the number of years since the analyst first appeared

in the I/B/E/S file. Firm-specific tenure is the number of years since the analyst began covering the specific firm in the

I/B/E/S file. Brokerage house size is the number of analysts in the analyst’s brokerage house. Firms covered is the number

of firms covered by the analyst. Panel B shows probit models predicting the HQ status indicator, which equals one if the

analyst is ranked as HQ in a given firm in the current year and zero otherwise (columns (1), (2), (5), and (6)) and the

regressions for the analyst’s closest absolute forecast error in a given firm in the current year in columns (3) and (4). HQ

status in other firms equals one (zero) if the analyst is of HQ in the majority of the other firms that the analyst follows

during the year; analysts who have an equal number of HQ and LQ rankings in other firms are excluded. Firm size is the

log of the firm’s market value of equity, equal to the stock price times the number of shares outstanding at the end of the

month prior to the annual earnings announcement. Annual return is the annual return of the firm's equity over the 12

months prior to the earnings announcement month. Leverage is the book value of total liabilities divided by the book

value of total assets, and Book-to-market is the book value of common equity divided by the market value of equity at

the end of the fiscal year. Number of analysts is the number of analysts following the firm. All independent variables are

measured prior to the announcement date. The probit coefficients are reported as marginal probability effects. All models

include the intercept. Robust standard errors are clustered by firm. z-statistics for probit models and t-statistics elsewhere

are in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

Panel A. HQ and LQ analyst characteristics

Analyst or announcement

characteristic HQ analysts LQ analysts

Difference

(t-statistic)

Overall tenure 7.07 7.00 0.07*** (4.73)

Firm-specific tenure 3.04 2.97 0.07*** (8.61)

Brokerage house size 65.76 63.04 2.72*** (19.14)

Firms covered 17.60 17.55 0.05* (1.79)

Absolute forecast error 0.0081 0.0089 -0.008*** (-12.83)

Forecast error 0.00185 0.00181 0.00004 (0.66)

44

Panel B. Persistence of analysts’ forecasting performance

HQ status Absolute forecast error HQ status

(1) (2) (3) (4) (5) (6)

HQ status (year t-1) 0.0414*** 0.0407*** -0.0007*** -0.0007*** 0.0531*** 0.0382***

(25.54) (25.13) (-16.14) (-15.91) (32.95) (22.84)

HQ status in other firms (year t-1) 0.0387*** 0.0514***

(23.14) (31.83)

Firm size 0.0034*** 0.0011*** -0.0061*** -0.0061***

(10.52) (3.11) (-25.12) (-25.15)

Annual return -0.0003 0.0005 -0.0009*** -0.0009***

(-0.50) (0.88) (-5.68) (-5.67)

Leverage 0.0006 0.0003 0.00573*** 0.0057***

(0.37) (0.20) (6.58) (6.55)

Book-to-market 0.0001 0.00003 0.00002 0.00002

(1.40) (0.54) (1.48) (1.48)

Number of analysts 0.0007*** 0.0007*** 0.00022*** 0.0002***

(12.40) (14.52) (10.78) (10.69)

Overall tenure 0.0007*** -0.00004*** 0.0002 (4.33) (-7.12) (1.12)

Firm-specific tenure 0.0023*** 0.00001 0.003***

(9.66) (1.45) (12.90)

Brokerage house size 0.0001*** -0.000001 0.0001***

(10.63) (-0.26) (7.23)

Firm coverage -0.0007*** 0.00003*** -0.0005***

(-12.32) (8.40) (-8.63)

Year fixed effects Yes Yes Yes Yes Yes Yes

Firm fixed effects Yes Yes

Observations (analyst-years) 485,815 485,815 485,815 485,815 443,262 443,262

Adj. R-squared 0.344 0.344

45

Table 2: The number of HQ analysts and the accuracy of their forecasts relative to the consensus Panel A compares the accuracy of the HQ analysts’ average forecast and the consensus forecast sorted by the number of

HQ analysts following the firm in a given earnings announcement year. Analysts are ranked as HQ based on their previous

year’s absolute forecast errors, defined in Table 1. The SUE of consensus (SUE of HQ analysts) is standardized

unexpected earnings, equal to the difference between the actual earnings and the average forecast provided by all analysts

(HQ analysts) following the firm normalized by the stock price at the beginning of the year. Absolute SUE is the absolute

value of SUE. Accuracy improvement is the percentage reduction from the absolute SUE of consensus to the absolute

SUE of HQ analysts. t-statistics in the last column are for the difference in the means test between the absolute SUEs of

the consensus and HQ analysts. Panel B reports sample characteristics, defined in Table 1, for two samples sorted based

on whether the firm is followed by fewer than four HQ analysts or four or more HQ analysts in a given announcement

year. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

Panel A. The smallest number of HQ analysts needed to improve over the consensus forecast

Number of

HQ analysts

Absolute SUE of

Consensus

Absolute SUE of

HQ analysts

Accuracy

improvement

t-statistics

Abs. SUE

difference

1 or more 0.00656 0.00678 -3.31% -8.63***

2 or more 0.00589 0.00595 -1.08% -3.19***

3 or more 0.00514 0.00513 0.19% 0.54

4 or more 0.00461 0.00455 1.17% 2.99***

5 or more 0.00422 0.00415 1.52% 3.51***

6 or more 0.00404 0.00396 1.96% 3.95***

7 or more 0.00386 0.00377 2.35% 4.47***

8 or more 0.00377 0.00367 2.69% 4.60***

9 or more 0.00355 0.00346 2.61% 3.91***

10 or more 0.00346 0.00337 2.59% 3.44***

46

Panel B: Comparing samples in which HQ analysts’ average forecast is either less or more

accurate than the consensus

Difference

(t-statistics)

Number of HQ analysts

4 or more Fewer than 4

Firm characteristics:

9,149*** (43.78) 10,522 1,372 Firm size ($M)

10.4*** (210.1) 16.7 6.3 Number of analysts

-0.67*** (-6.49) 0.66 1.34 Book-to-market

0.04** (14.93) 0.57 0.53 Leverage

-1.3* (-1.74) 20.4 21.7 Annual return (%)

891 1136 Avg. number of firms per year

Analyst characteristics:

0.51*** (8.66) 7.42 6.91 Overall tenure

1.10*** (29.48) 3.43 2.33 Firm-specific tenure

12.3*** (18.73) 69.4 57.1 Brokerage house size

0.5*** (3.73) 18.2 17.7 Firms covered

47

Table 3: The immediate reaction to earnings announcements This table reports the earnings response coefficients for measures of earnings surprise (SUE) based on the forecasts of all

analysts following the firm (consensus) and on the forecasts of high- and low-quality (HQ and LQ) analysts. Analysts are

ranked as HQ or LQ based on their previous year’s absolute forecast errors, defined in Table 1. The dependent variable is

the buy-and-hold abnormal return (based on the four-factor Fama-French and Carhart model) for the earnings

announcement day and the following trading day. The SUE of Consensus and SUE of HQ and LQ analysts are defined in

Table 2. All other variables are defined in Table 1. Columns (1)-(3) use the entire sample of earnings announcements, and

columns (4)-(6) use the sample of earnings announcements by firms followed by at least four HQ analysts. All independent

variables other than SUE are measured prior to the announcement date. The intercept and year fixed effects are included

in all regressions. Robust standard errors are clustered by firm. t-statistics are provided in parentheses. The last two lines

report the p-values for the chi-squared tests of the equality of the coefficients on SUE measures for the three analyst groups.

*, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

Full Sample 4 or more HQ analysts

(1) (2) (3) (4) (5) (6)

SUE of Consensus 0.7245*** 0.7526*** (13.62) (5.20)

SUE of HQ analysts 0.6211*** 0.6927***

(12.93) (5.12)

SUE of LQ analysts 0.5691*** 0.6044*** (12.78) (4.85)

Firm size -0.0003 -0.0002 -0.0001 -0.0007 -0.0007 -0.0007 (-0.71) (-0.55) (-0.37) (-1.19) (-1.15) (-1.14)

Annual return -0.0006 -0.0006 -0.0006 0.0007 0.0007 0.0007 (-0.98) (-0.89) (-0.87) (0.68) (0.72) (0.71)

Leverage 0.0059*** 0.0057*** 0.0057*** 0.0030 0.0029 0.0028 (3.73) (3.55) (3.56) (1.24) (1.19) (1.12)

Book-to-market 0.00002 0.00001 0.00001 -0.0002*** -0.00018*** -0.00023*** (0.38) (0.29) (0.28) (-9.20) (-7.67) (-11.14)

Number of analysts 0.00002 0.00002 0.00001 -0.00004 -0.00003 -0.00004 (0.25) (0.28) (0.08) (-0.42) (-0.40) (-0.45)

Observations 44,709 44,709 44,709 20,221 20,221 20,221

Adj. R-squared 0.015 0.013 0.013 0.011 0.010 0.009

p-value (SUE of HQ

analysts vs. SUE of

consensus)

0.000 0.009

p-value (SUE of HQ

analysts vs. SUE of LQ

analysts)

0.02 0.01

48

Table 4: Predicting market reaction on the earnings announcement day The dependent variable is the buy-and-hold abnormal return (based on the four-factor Fama-French and Carhart model)

for the earnings announcement day and the following trading day. Analysts are ranked as HQ or LQ based on their

previous year’s absolute forecast errors, defined in Table 1. Predicted surprise is equal to (HQ analysts’ average forecast

minus the consensus forecast) in columns (1) and (2) and (HQ analysts’ average forecast minus LQ analysts’ average

forecast) in columns (3) and (4), normalized by the stock price at the beginning of the year. The positive predicted surprise

indicator equals one if predicted surprise is positive and zero if it is negative. Big positive predicted surprise equals one

if predicted surprise is greater than the median of positive values of predicted surprise and zero if predicted surprise is

smaller than the median of the negative values of predicted surprise in year t-1. All independent variables are measured

prior to the announcement date, and the regressions include the intercept and year fixed effects. Robust standard errors

are clustered by firm. t-statistics are provided in parentheses. The last line of the table provides the two-day holding

returns of a trading strategy that is long if the predicted surprise indicator variable in that column is equal to 1 and short

if it is equal to 0. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

Predicted surprise:

HQ average – Consensus

Predicted surprise:

HQ average – LQ average

(1) (2) (3) (4)

Positive predicted surprise 0.0015* 0.0019**

(1.92) (2.48)

Big positive predicted surprise 0.0007* 0.0008**

(1.71) (1.98)

Firm size 0.0003 -0.00002 0.0003 -0.00002 (0.76) (-0.03) (0.75) (-0.04)

Annual return -0.0002 -0.0006 -0.0002 -0.0010 (-0.25) (-0.67) (-0.24) (-1.15)

Leverage 0.0040** 0.0071*** 0.0040** 0.0072*** (2.45) (2.89) (2.45) (2.90)

Book-to-market 0.00001 0.00001 0.00001 0.00001 (0.03) (0.15) (0.03) (0.11)

Number of analysts -0.00001 -0.00006 -0.00001 -0.00002

(-0.02) (-0.51) (-0.04) (-0.15)

Observations 44,709 20,999 44,709 20,605

Adj. R-squared (%) 0.086 0.078 0.171 0.230

Two-day long-short strategy

returns (%)

0.14*

(1.88)

0.20*

(1.64)

0.19**

(2.52)

0.24*

(1.94)

49

Table 5: Returns following recommendation revisions The dependent variable is the firm’s stock return in the calendar month following the month with a recommendation

revision. The sample consists of all recommendation revisions in the month when the annual earnings is announced by

the firm. A recommendation is an integer from 1 to 5, where 1 is strong buy, 5 is strong sell, and 3 is hold. A

recommendation revision is the negative of the difference between the current and the previous recommendations of an

analyst; thus, a positive (negative) recommendation revision is an upgrade (downgrade). The consensus, HQ, and LQ

recommendation revision variables are the averages of individual analysts’ revisions of all, HQ, and LQ analysts

following the firm, respectively, during the earnings announcement month. Analysts are ranked as HQ or LQ based on

this year’s absolute forecast errors, defined in Table 1. HQ-consensus is equal to HQ analysts’ average recommendation

revision minus the consensus recommendation revision if HQ analysts’ average recommendation revision is either

positive and greater or negative and smaller (more negative) than the consensus recommendation revision; otherwise, this

variable is zero. The other independent variables are defined in Table 1 and measured prior to the earnings announcement.

All regressions include the intercept, and robust standard errors are clustered by firm. The last two lines provide the event-

time raw long-short strategy returns and calendar-time alphas of the value-weighted long-short portfolio based on the

four-factor Fama-French and Carhart model in the month following the month with the revision. The long (short) position

is in the firms for which the mean recommendation revision is positive (negative), according to the consensus, HQ, and

LQ analysts’ recommendation revision variables in columns (1)-(3), respectively. In column (4), the position in the stock

is long (short) if HQ-consensus is positive (negative); otherwise, the stock does not enter either portfolio. t-statistics are

provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

(1) (2) (3) (4)

Consensus recommendation revision 0.0015*

(1.67)

HQ analysts’ recommendation revision 0.0025**

(2.09)

LQ analysts’ recommendation revision 0.0004

(0.30)

HQ-consensus 0.0158***

(2.62)

Lagged dependent variable 0.0141 0.0143 0.0158 0.0161

(1.01) (1.04) (1.15) (1.19)

Firm size -0.0043*** -0.0043*** -0.0043*** -0.0043***

(-4.26) (-4.25) (-4.20) (-4.20)

Leverage 0.0008 0.0008 0.0007 0.0008

(0.18) (0.19) (0.16) (0.19)

Book-to-market -0.00001 -0.00001 -0.00001 -0.00001

(-0.34) (-0.30) (-0.32) (-0.32)

Number of analysts 0.0003* 0.0003* 0.0003* 0.0003*

(1.80) (1.81) (1.78) (1.78)

Year fixed effects Yes Yes Yes Yes

Observations 21,381 21,381 21,381 21,381

Adj. R-squared 0.0430 0.0420 0.0419 0.0421

Long-short raw return next month (%) 0.36 0.85*** 0.14 1.24***

(1.61) (3.11) (0.49) (3.34)

Long-short monthly calendar-time alpha (%) -0.16

(-0.45)

0.32

(0.79)

-0.31

(-0.71)

1.06*

(1.80)

50

Table 6: Forecast dispersion and future return volatility The dependent variable is the standard deviation of the firm’s daily returns in the month following the

annual earnings announcement month. Consensus, HQ, and LQ analysts’ forecast dispersion are the

standard deviation of the consensus, HQ, and LQ analysts’ forecasts, respectively, normalized by the

stock price and using each analyst’s closest forecast issued during the 60 days prior to the earnings

announcement. Analysts are ranked as HQ or LQ based on their previous year’s absolute forecast errors,

defined in Table 1. The other independent variables are defined in Table 1 and measured prior to the

announcement date. All regressions include the intercept. Robust standard errors are clustered by firm.

t-statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level,

respectively.

(1) (2) (3)

Consensus dispersion 0.0730

(1.63)

HQ analysts’ dispersion 0.1315**

(2.55)

LQ analysts’ dispersion 0.0340

(0.79)

Lagged dependent variable 0.5179*** 0.5141*** 0.5206***

(12.69) (12.82) (12.63)

Firm size -0.0007 -0.0006 -0.0008*

(-1.59) (-1.40) (-1.73)

Annual return 0.0002 0.0002 0.0002

(0.53) (0.56) (0.46)

Leverage -0.0007 -0.0007 -0.0005

(-0.29) (-0.31) (-0.23)

Book-to-market 0.0015 0.0016 0.0015

(1.25) (1.41) (1.16)

Number of analysts -0.00004 -0.00004 -0.00003

(-1.22) (-1.40) (-1.13)

Year fixed effects Yes Yes Yes

Firm fixed effects Yes Yes Yes

Observations 4,812 4,812 4,812

Adj. R-squared 0.691 0.693 0.691

51

Table 7: Post-earnings announcement drift and analysts’ uncertainty The table reports the monthly abnormal returns for 1- to 11-month horizons following annual earnings

announcements. Announcements are divided into two subsamples in which the standard deviation of HQ

analysts’ forecast errors is greater (the high-uncertainty sample) or smaller (the low-uncertainty sample) than the

standard deviation of forecast errors for all analysts following the firm. Analysts are ranked as HQ based on their

previous year’s absolute forecast errors, defined in Table 1. A stock is assigned to the long or short portfolio,

depending on whether its earnings surprise is positive or negative, respectively, where earnings surprise is defined

based on the consensus estimate in Table 2. A stock enters a portfolio at the beginning of the month following

the month of the announcement and is held for the length of the horizon. In columns (1)-(6), the monthly value-

weighted portfolio returns are regressed on the four Fama-French-Carhart factors to obtain the reported drift,

which is the intercept of the regression (monthly alpha). For the monthly alphas reported in column (7), the high-

uncertainty long-short post-announcement raw return is regressed on the full-sample long-short post-

announcement raw return and the four Fama-French-Carhart factors. *, **, and *** represent 10%, 5%, 1%,

significance based on the regression t-statistics, respectively.

PEAD horizon

(months)

High uncertainty Low uncertainty High

uncertainty

relative to

full sample Long Short

Long-

Short Long Short

Long-

Short

(1) (2) (3) (4) (5) (6) (7)

1 1.09 -0.35 1.44* -0.46 0.30 -0.76 1.18**

2 1.36*** -0.12 1.48** 0.13 0.33 -0.20 1.17*

3 1.87*** -0.58 2.46*** 0.20 0.19 0.01 1.48**

4 1.06*** 0.04 1.02 -0.27 0.35 -0.62 0.81

5 0.90*** 0.18 0.72 -0.05 -0.35 0.30 0.43

6 1.19*** -0.40 1.58*** -0.03 -0.20 0.17 1.19***

7 0.97*** -0.35 1.42*** -0.16 0.07 -0.23 1.10***

8 0.97*** -0.48* 1.45*** -0.18 -0.22 0.04 1.18***

9 0.50*** -0.56** 1.06*** -0.14 -0.22 0.09 0.80**

10 0.42*** -0.44** 0.85*** -0.08 -0.33 0.25 0.59**

11 0.41*** -0.44** 0.85*** 0.03 -0.4** 0.37* 0.32*

52

Table 8: Analysts’ outputs at the aggregate level The dependent variables are the monthly value-weighted market returns (Panel A) and the returns on the VIX (Panel B)

for the calendar month following the month with the earnings announcement. The main explanatory variables in Panel A

are based on the recommendation revisions during the earnings announcement month, defined in Table 5. The consensus,

HQ, and LQ mean recommendation revision variables are the sums of all, HQ, and LQ analysts’ revisions, respectively,

divided by the number of revisions for all firms with an earnings announcement in that calendar month. The HQ-

consensus mean recommendation revision is the HQ mean recommendation revision minus the consensus mean

recommendation revision if the HQ mean recommendation revision is either positive and greater or negative and smaller

than the consensus recommendation revision; otherwise, this variable is zero. In Panel B, forecast dispersion is a value-

weighted average of firm-level analysts’ forecast error dispersions prior to the earnings announcement, defined in Table

6, with the firms’ market capitalizations as the weights. Analysts are ranked as HQ or LQ based on this year’s (Panel A)

and the previous year’s (Panel B) absolute forecast errors, defined in Table 1. The dispersion ratio of HQ (LQ) analysts

is the value-weighted average of firms’ ratios of HQ (LQ) analysts’ dispersion to Consensus dispersion. The control

variables are the monthly earnings-to-price ratio, dividend-to-price ratio, term spread, default spread, one-month T-bill

rate, 30-year Treasury yield, rate of inflation, and change in economic policy uncertainty (EPU), defined in Section 2.

The models use Newey-West standard errors with three lags in Panel A and Huber-White robust standard errors in Panel

B. The last row in Panel A reports the market model alphas obtained as follows. In Panel A, the alphas are from regressing

a long-short market-holding strategy return on the market return, where the market-holding strategy is the following. In

columns (5)-(7), long (short) the next month’s market return if the consensus, HQ, or LQ analysts’ mean recommendation

revision of that column is greater (smaller) than the median of the respective mean recommendation revision over the

previous 24 months; in column (8), long (short) the next month’s market return if the HQ-consensus mean

recommendation revision is positive (negative), and have a zero position in the market index if the HQ-consensus is zero.

The last line in Panel B provides the alphas from regressing the VIX strategy return on the market return, where the VIX

strategy return is a long or short VIX return, depending on whether the column’s dispersion or dispersion ratio last month

is greater or smaller than the median of the dispersion or dispersion ratio over the previous 24 months, respectively. t-

statistics are provided in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

53

Panel A: Predicting market returns

(1) (2) (3) (4) (5) (6) (7) (8)

Consensus mean 0.016* 0.015*

recommendation revision (1.85) (1.87)

HQ analysts’ mean 0.017** 0.017**

recommendation revision (2.25) (2.44)

LQ analysts’ mean 0.005 0.004

recommendation revision (0.91) (0.70)

HQ-consensus mean 0.027* 0.028*

recommendation revision (1.89) (1.89)

Lagged dependent 0.073 0.073 0.070 0.068 0.050 0.055 0.047 0.050

variable (0.93) (0.96) (0.90) (0.91) (0.73) (0.80) (0.68) (0.75)

Earnings-to-price ratio -0.148 -0.120 -0.175 -0.140

(-0.51) (-0.41) (-0.60) (-0.47)

Dividend-to-price ratio 1.913** 1.869** 1.968** 1.936**

(2.45) (2.40) (2.48) (2.45)

Term spread 0.679** 0.665* 0.647* 0.614*

(1.99) (1.94) (1.93) (1.81)

Default spread -1.733 -1.583 -1.857* -1.678

(-1.65) (-1.51) (-1.75) (-1.58)

One-month T-bill yield 3.308 3.136 3.323 3.025

(1.34) (1.24) (1.36) (1.18)

Long-term T-bond yield 0.091 0.100 0.090 0.105

(1.28) (1.44) (1.26) (1.52)

Inflation 0.470 0.437 0.544 0.499

(0.64) (0.61) (0.74) (0.70)

Intercept 0.009*** 0.010*** 0.008*** 0.008*** 0.028 0.026 0.026 0.022

(3.44) (3.59) (2.78) (2.93) (1.08) (1.02) (1.03) (0.90)

Observations 265 265 265 265 265 265 265 265

Adj. R-squared 0.09 0.018 -0.001 0.011 0.028 0.037 0.018 0.031

Monthly alpha (%) 0.42

(1.44)

0.49*

(1.65)

0.31

(1.06)

0.57***

(2.60)

54

Panel B: Predicting changes in market volatility

(1) (2) (3) (4) (5)

Consensus dispersion 2.104

(0.35)

HQ analysts’ dispersion 5.345

(0.64)

LQ analysts’ dispersion 2.625

(0.39)

Dispersion ratio of HQ analysts 0.107*

(1.91)

Dispersion ratio of LQ analysts -0.010

(-0.28)

Lagged dependent variable -0.046 -0.045 -0.047 -0.040 -0.047

(-0.36) (-0.36) (-0.36) (-0.30) (-0.36)

EPU change 0.060 0.062 0.061 0.068 0.059

(1.00) (1.04) (1.02) (1.16) (0.98)

Value-weighted market return 0.576 0.592 0.591 0.518 0.545

(1.40) (1.44) (1.43) (1.24) (1.33)

Earnings-to-price ratio -1.109 -1.075 -1.078 -1.560 -1.195

(-0.80) (-0.77) (-0.77) (-1.07) (-0.86)

Dividend-to-price ratio 1.244 0.865 1.092 3.567 1.919

(0.31) (0.22) (0.26) (0.88) (0.49)

Term spread 1.130 1.020 1.044 1.828 1.363

(0.57) (0.51) (0.51) (0.87) (0.67)

Default spread -4.540 -4.347 -4.523 -6.245 -5.034

(-0.85) (-0.82) (-0.85) (-1.14) (-0.94)

One-month T-bill yield 7.197 6.844 6.563 8.362 7.834

(0.52) (0.49) (0.47) (0.60) (0.55)

Long-term T-bond yield -0.150 -0.176 -0.134 -0.246 -0.155

(-0.37) (-0.43) (-0.33) (-0.61) (-0.38)

Inflation -2.114 -2.338 -2.194 -1.974 -1.832

(-0.53) (-0.58) (-0.54) (-0.50) (-0.46)

Intercept 0.127 0.120 0.123 0.075 0.150

(0.77) (0.73) (0.74) (0.47) (0.87)

Observations 197 197 197 197 197

Adj. R-squared (%) 0.038 0.041 0.038 0.056 0.037

Obs. in Long portfolio 115 124 74 141 64

Obs. in Short portfolio 97 88 138 71 148

Monthly alpha (%) 1.85 2.04 -0.57 3.32*** -0.56

(1.34) (1.60) (-0.40) (2.68) (-0.41)